Phony Permutation

You are given an array of integers $A$ formed by concatenating the identity permutation of length $N$ exactly $K$ times. For given positive integers $a, b, c$ and $d$, the score $S$ of a sequence $[s_{1}, s_{2}, \ldots , s_{l}]$ is defined as : $ S = \frac{(g + a) \times (g + b)}{(l + c) \times (l + d)} $ where $g$ denotes the GCD of the sequence and $l$ denotes the length of the sequence. F